A beam is a horizontal structural element that is capable of withstanding load by resisting bending. Hence, beams are flexural members, therefore, Bending Strength or flexural strength, which is a product of Young’s modulus (E) and Moment of Inertia (I) is an important parameter for beams.
Behaviour of the beam is primarily observed by deflection and cracking. Deflection of beams depends on various factors like type of beam, type of loading, type of material, span and shape of cross-section.
Primarily, beams take transverse loading which generates shear force and bending moment. Hence beams are analyzed by SFD and BMD.
Depending on the types of support conditions, beams are classified as
- Simply Supported Beam
- Continuous Beam
- Cantilever Beam
- Fixed Beam
Different types of loadings on the beams are
- Concentrated Load or Point Load
- Uniformly Distributed Load
- Uniformly Varied Load
We shall see the behaviour of different types of beams of same span length considering Uniformly Distributed Transverse loading
Page Contents
SIMPLY SUPPORTED BEAM
A simply supported beam carrying a uniformly distributed load bend in such a way that it produces tension at bottom i.e., it bends with concavity upwards.
It is subjected to maximum positive bending moment (sagging) at its mid span where shear force is zero while the moment is zero at supports. Maximum displacement is also seen at the mid span.
{Simply Supported beams are statically determinate}
CONTINUOUS BEAM
Introduction of one or more supports in a simply supported beam makes it continuous beam.
Bending moment is still zero at its extreme ends. And the deflection curve passing over the intermediate supports produces tension at the top. The positive bending moment is maximum not at the mid-span but a small distance towards the end. After this, it reduces to zero and the curvature changes to hogging from sagging.
Beams are made continuous in order to reduce the sagging or positive bending moment and develop hogging or negative bending moment at the intermediate support thereby Point of Contraflexure (POC) (Point of Inflection) is obtained somewhere near the support.
As a result, the load carrying capacity is increased and deflection is reduced when compared with simply supported beam of same span. {Continuous Beams are statically indeterminate}
CANTILEVER BEAM
In the previous two cases the supports are simply supported which means the supports does not allow any transverse movement of the beam but it allows rotation and hence there is no moment developed at the support. But in case of a FIXED SUPPORT, both movement and rotation are restrained.
A cantilever beam is one in which one end of the beam is completely fixed and the other end is free. This kind of beams are generally used in balconies where only one end is supported and the other end is free (although complete fixity is not achieved in real construction).
When such beams are subjected to UDL, the support takes the maximum load and as a result, Shear Force and Bending Moment are maximum at the support and zero at the free end.
In contrast to the simply supported beam where sagging moment is developed (tension at the bottom), here hogging moment (tension at the top) is developed.
{Generally, reinforcements are provided at the tension zone. Hence the main reinforcement in case of a cantilever beam is provided at the top face of the beam whereas in case of a simply supported beam it is provided at the bottom face.}
FIXED BEAM
When both ends of the beam are restrained against movement and rotation, it is called as a fixed beam.
Now when a UDL is applied throughout a fixed beam both sagging and hogging moments develop. Being fixed both ends develop shear force and also Bending Moment at the supports.
Maximum Hogging moment is developed at the supports and the maximum sagging moment is developed at the midspan. Somewhere between the midspan and the support, Point of Contraflexure (POC) is observed (The point where moment changes its sign i.e., from hogging to sagging).
Maximum deflection is seen at the mid span where zero shear and maximum positive bending moment is observed. Deflection of a fixed beam is comparatively lesser than Simply Supported beam
{Generally, for a fixed beam, POC occurs at a distance of 0.211L (L – length of the beam) from both the ends. Thus, a fixed beam has two points of contraflexure}
POINTS TO REMEMBER
When the span length and the loading type is considered constant,
- Maximum Positive Bending moment and maximum deflection is observed at a point where Shear force is zero.
- Maximum displacement is seen for cantilever beam followed by Simply Supported beam while Continuous beam shows less displacement.
- Bending Moment (both positive and negative) and Shear force is least for a Continuous beam than any other type.